Functional-integral approach to chiral anomalies in supersymmetric gauge theories

Konishi, Kenichi; Shizuya, K.

doi:10.1007/bf02724227

Cited by 160 publications

(181 citation statements)

References 26 publications

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“…Note that auxiliary fields have vanishing weights and hence do not contribute. We find Again the instanton background gives a t-independent result EB 2(cosh 2tE + cosh 2tB) − 2 − cosh t(E + B) − cosh t(E − B) sinh tE sinh tB = 6EB, (B 13) and hence the Jacobian is exact for F -terms but not for higher-dimensional D-terms.…”

Section: B Trace Anomaliesmentioning

confidence: 88%

“…The only possible gauge covariant extension is e t(Dµ) 2 because the auxiliary component transforms the same way as the other components under the ordinary gauge transformations. We will see later that this regularization of the components can be justified in a manifestly supersymmetric way [13], but the above arguments are a quick route to the correct answer.…”

Section: A3 Chiral Multipletsmentioning

confidence: 89%

“…As with the vector multiplet, however, the measure is not invariant under this change, and there is an anomalous Jacobian [13]. In our case, Z i (M, M ′ ) is real, but it is sensible to look at D(Z −1/2 φ ′ ) for a general complex Z since φ ′ is a chiral superfield.…”

Section: Models With Matter Fieldsmentioning

confidence: 91%

“…Even though we have used component calculations, we must mention that the Gaussian regularization we used in this subsection can be made manifestly supersymmetric, as was done originally in [13]: 27) where the factor −D 2 /4 restricts the trace over the superspace only to the chiral one, with * *…”

Section: A3 Chiral Multipletsmentioning

confidence: 99%

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Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Arkani-Hamed

Murayama

2000

J. High Energy Phys.

197

278

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There have long been known "exact" β functions for the gauge coupling in N = 1 supersymmetric gauge theories, the so-called Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β functions. Shifman and Vainshtein further related these β functions to the exact 1-loop running of the gauge coupling in a "Wilsonian" action. All these results, however, remain somewhat mysterious. We attempt to clarify these issues by presenting new perspectives on the NSVZ β function. Our interpretation of the results is somewhat different than the one given by Shifman and Vainshtein, having nothing to do with the distinction between "Wilsonian" and "1PI" effective actions. Throughout we work in the context of the Wilsonian Renormalization Group; namely, as the cutoff of the theory is changed from M to M ′ , we seek to determine the appropriate changes in the bare couplings needed in order to keep the low energy physics fixed. The entire analysis is therefore free of infrared subtleties. When the bare Lagrangian given at the cutoff is manifestly holomorphic in the gauge coupling, we show that the required change in the holomorphic gauge coupling is exhausted at 1-loop to all orders of perturbation theory, and even non-perturbatively in some cases. On the other hand, when the bare Lagrangian at the cutoff has canonically normalized kinetic terms, we find that the required change in the gauge coupling is given by the NSVZ β function. The higher order contributions in the NSVZ β function are due to anomalous Jacobians under the rescaling of the fields done in passing from holomorphic to canonical normalization. We also give prescriptions for regularizing certain N = 1 theories with an ultraviolet cutoff M preserving manifest holomorphy, starting from finite N = 4 and N = 2 theories. It is then at least in principle possible to check the validity of the exact β function by higher order calculations in these theories. * This work was supported in part by the

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Section: B Trace Anomaliesmentioning

confidence: 88%

Section: A3 Chiral Multipletsmentioning

confidence: 89%

Section: Models With Matter Fieldsmentioning

confidence: 91%

Section: A3 Chiral Multipletsmentioning

confidence: 99%

See 2 more Smart Citations

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Arkani-Hamed

Murayama

2000

J. High Energy Phys.

197

278

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“…Even if classically the mesons vanish, at the quantum level their expectation value is set by the Konishi anomaly to Q f Q f = N f S/m, where S is the glueball superfield [5]. The effective glueball superpotential is recovered by integrating this exact expectation value with respect to the corresponding coupling.…”

Section: Introductionmentioning

confidence: 99%

Chiral Rings, Anomalies and Electric-Magnetic Duality

Mazzucato

2004

J. High Energy Phys.

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We study electric-magnetic duality in the chiral ring of a supersymmetric U (N c ) gauge theory with adjoint and fundamental matter, in presence of a general confining phase superpotential for the adjoint and the mesons. We find the magnetic solution corresponding to both the pseudoconfining and higgs electric vacua. By means of the Dijkgraaf-Vafa method, we match the effective glueball superpotentials and show that in some cases duality works exactly offshell. We give also a picture of the analytic structure of the resolvents in the magnetic theory, as we smoothly interpolate between different higgs vacua on the electric side.

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Konishi anomalies and N = 1 curves

Landsteiner

2005

Fortschritte der Physik

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We present a brief summary of exact results on the non-perturbative effective superpotential of N = 1 supersymmetric gauge theories based on generalized Konishi anomaly equations. In particular we consider theories with classical gauge groups and chiral matter in two-index tensor representations. All these theories can be embedded into theories with unitary gauge group and adjoint matter. This embedding can be used to derive expressions for the exact non-perturbative superpotential in terms of the 1/N expansion of the free energy of the related matrix models.

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Functional-integral approach to chiral anomalies in supersymmetric gauge theories

Cited by 160 publications

References 26 publications

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Chiral Rings, Anomalies and Electric-Magnetic Duality

Konishi anomalies and N = 1 curves

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